Using Higher Levels of Abstraction for Solving Optimization Problems by Boolean Satisfiability

Optimization problems can be solved using Boolean Satisfiability by mapping them to a sequence of decision problems. Therefore, in the last years several encodings have been developed. Independently, also new solvers have been introduced lifting Boolean Satisfiability to higher levels of abstraction, e.g. SAT Modulo Theories (SMT) solvers and word level solvers. Both support bit-vector logic and thus allow more compact encodings of the problems. In this paper we investigate the efficiency of these new solver paradigms applied to optimization problems. We show for two case studies - graph coloring and exact synthesis of reversible logic - that the resulting problem instances can be reduced with respect to the size. In addition for the synthesis problem significant run-time improvements can be achieved.